Roberto Casadio | Università di Bologna (original) (raw)

Papers by Roberto Casadio

Journal of High Energy Physics, 2015

We study the nature of the inner Cauchy horizon of a Reissner-Nordström black hole in a quantum c... more We study the nature of the inner Cauchy horizon of a Reissner-Nordström black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function. Our main finding it that there is a significant range of black hole mass (around the Planck scale) and specific charge for which the probability of realizing the inner horizon is negligible. This result suggests that any semiclassical instability one expects near the inner horizon may not be occur in quantum black holes.

EPL (Europhysics Letters), 2015

ABSTRACT We consider a solution of the effective four-dimensional brane-world equations, obtained... more ABSTRACT We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of General Relativity in the Solar system.

The minimal geometric deformation approach was introduced in order to study the exterior space-ti... more The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application.

The minimal geometric deformation approach was introduced in order to study the exterior space-ti... more The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application.

Physics Letters B, 2015

We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) forma... more We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio α > 1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α 2 < 2, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for α 2 > 2, and the uncertainty in the location of the horizon blows up at α 2 = 2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of √ 2) can exist.

We apply several methods related to the WKB approximation to study cosmological perturbations dur... more We apply several methods related to the WKB approximation to study cosmological perturbations during inflation, obtaining the full power spectra of scalar and tensor perturbations to first and to second order in the slow-roll parameters. We compare our results with those derived by means of other methods, in particular the Green's function method, and find agreement for the slow-roll structure.

We study modifications of the Hawking emission in the evaporation of miniature black holes possib... more We study modifications of the Hawking emission in the evaporation of miniature black holes possibly produced in accelerators when their mass approaches the fundamental scale of gravity, set to 1 TeV according to some extra dimension models. Back-reaction and quantum gravity corrections are modelled by employing modified relations between the black hole mass and temperature. We release the assumption that

The Twelfth Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity Astrophysics and Relativistic Field Theories - Proceedings of the MG12 Meeting on General Relativity, 2012

Over the last few years, it was realised that non-canonical scalar fields can lead to the acceler... more Over the last few years, it was realised that non-canonical scalar fields can lead to the accelerated expansion in the early universe. The primordial spectrum in these scenarios not only shows near scale-invariance consistent with CMB observations, but also large primordial non-Gaussianity. Second-order perturbation theory is the primary theoretical tool to investigate such non-Gaussianity. However, it is still uncertain which quantities are gauge-invariant at second-order and their physical understanding therefore remains unclear. As an attempt to understand second order quantities, we consider a general noncanonical scalar field, minimally coupled to gravity, on the unperturbed FRW background where metric fluctuations are neglected a priori. In this simplified set-up, we show that there arise ambiguities in the expressions of physically relevant quantities, such as the effective speeds of the perturbations. Further, the stress tensor and energy density display a potential instability which is not present at linear order.

Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers th... more Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running

A particle in four dimensions should behave like a classical black hole if the horizon radius is ... more A particle in four dimensions should behave like a classical black hole if the horizon radius is larger than the Compton wavelength or, equivalently, if its degeneracy (measured by entropy in units of the Planck scale) is large. For spherically symmetric black holes in 4 + d dimensions, both arguments again lead to a mass threshold MC and degeneracy scale M deg of the order of the fundamental scale of gravity MG. In the brane-world, deviations from the Schwarzschild metric induced by bulk effects alter the horizon radius and effective four-dimensional Euclidean action in such a way that MC ≃ M deg might be either larger or smaller than MG. This opens up the possibility that black holes exist with a mass smaller than MG and might be produced at the LHC even if MG 10 TeV, whereas effects due to bulk graviton exchanges remain undetectable because suppressed by inverse powers of MG. Conversely, even if black holes are not found at the LHC, it is still possible that MC ≫ MG and MG ≃ 1 TeV.

Journal of High Energy Physics, 2010

We analyse a family of brane-world black holes which solve the effective four-dimensional Einstei... more We analyse a family of brane-world black holes which solve the effective four-dimensional Einstein equations for a wide range of parameters related to the unknown bulk/brane physics. We first constrain the parameters using known experimental bounds and, for the allowed cases, perform a numerical analysis of their time evolution, which includes accretion through the Earth. The study is aimed at

The minimal geometric deformation approach is employed to show the existence of braneworld stella... more The minimal geometric deformation approach is employed to show the existence of braneworld stellar distributions with vacuum Schwarzschild exterior, thus without energy leaking from the exterior of the brane-world star into the extra dimension. The interior satisfies all elementary criteria of physical acceptability for a stellar solution, namely, it is regular at the origin, the pressure and density are positive and decrease monotonically with increasing radius, finally all energy conditions are fulfilled. A very thin solid crust with negative radial pressure separates the interior from the exterior, having a thickness ∆ inversely proportional to both the brane tension σ and the radius R of the star, i.e. ∆ −1 ∼ R σ. This brane-world star with Schwarzschild exterior would appear only thermally radiating to a distant observer and be fully compatible with the stringent constraints imposed on stellar parameters by observations of gravitational lensing, orbital evolutions or properties of accretion disks. * jovalle@usb.ve † laszlo.a.

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking tempera... more We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

A localised particle in Quantum Mechanics is described by a wave packet in position space, regard... more A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.

Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investi... more Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.

International Journal of Modern Physics D, 2009

It has recently been debated whether a class of generalized uncertainty principles that include g... more It has recently been debated whether a class of generalized uncertainty principles that include gravitational sources of error is compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the

Quantum Aspects of Black Holes, 2014

We review the main consequences of the possible existence of a minimum measurable length, of the ... more We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures.

Journal of High Energy Physics, 2015

We study the nature of the inner Cauchy horizon of a Reissner-Nordström black hole in a quantum c... more We study the nature of the inner Cauchy horizon of a Reissner-Nordström black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function. Our main finding it that there is a significant range of black hole mass (around the Planck scale) and specific charge for which the probability of realizing the inner horizon is negligible. This result suggests that any semiclassical instability one expects near the inner horizon may not be occur in quantum black holes.

EPL (Europhysics Letters), 2015

ABSTRACT We consider a solution of the effective four-dimensional brane-world equations, obtained... more ABSTRACT We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of General Relativity in the Solar system.

The minimal geometric deformation approach was introduced in order to study the exterior space-ti... more The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application.

The minimal geometric deformation approach was introduced in order to study the exterior space-ti... more The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application.

Physics Letters B, 2015

We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) forma... more We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio α > 1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α 2 < 2, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for α 2 > 2, and the uncertainty in the location of the horizon blows up at α 2 = 2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of √ 2) can exist.

We apply several methods related to the WKB approximation to study cosmological perturbations dur... more We apply several methods related to the WKB approximation to study cosmological perturbations during inflation, obtaining the full power spectra of scalar and tensor perturbations to first and to second order in the slow-roll parameters. We compare our results with those derived by means of other methods, in particular the Green's function method, and find agreement for the slow-roll structure.

We study modifications of the Hawking emission in the evaporation of miniature black holes possib... more We study modifications of the Hawking emission in the evaporation of miniature black holes possibly produced in accelerators when their mass approaches the fundamental scale of gravity, set to 1 TeV according to some extra dimension models. Back-reaction and quantum gravity corrections are modelled by employing modified relations between the black hole mass and temperature. We release the assumption that

The Twelfth Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity Astrophysics and Relativistic Field Theories - Proceedings of the MG12 Meeting on General Relativity, 2012

Over the last few years, it was realised that non-canonical scalar fields can lead to the acceler... more Over the last few years, it was realised that non-canonical scalar fields can lead to the accelerated expansion in the early universe. The primordial spectrum in these scenarios not only shows near scale-invariance consistent with CMB observations, but also large primordial non-Gaussianity. Second-order perturbation theory is the primary theoretical tool to investigate such non-Gaussianity. However, it is still uncertain which quantities are gauge-invariant at second-order and their physical understanding therefore remains unclear. As an attempt to understand second order quantities, we consider a general noncanonical scalar field, minimally coupled to gravity, on the unperturbed FRW background where metric fluctuations are neglected a priori. In this simplified set-up, we show that there arise ambiguities in the expressions of physically relevant quantities, such as the effective speeds of the perturbations. Further, the stress tensor and energy density display a potential instability which is not present at linear order.

Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers th... more Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running

A particle in four dimensions should behave like a classical black hole if the horizon radius is ... more A particle in four dimensions should behave like a classical black hole if the horizon radius is larger than the Compton wavelength or, equivalently, if its degeneracy (measured by entropy in units of the Planck scale) is large. For spherically symmetric black holes in 4 + d dimensions, both arguments again lead to a mass threshold MC and degeneracy scale M deg of the order of the fundamental scale of gravity MG. In the brane-world, deviations from the Schwarzschild metric induced by bulk effects alter the horizon radius and effective four-dimensional Euclidean action in such a way that MC ≃ M deg might be either larger or smaller than MG. This opens up the possibility that black holes exist with a mass smaller than MG and might be produced at the LHC even if MG 10 TeV, whereas effects due to bulk graviton exchanges remain undetectable because suppressed by inverse powers of MG. Conversely, even if black holes are not found at the LHC, it is still possible that MC ≫ MG and MG ≃ 1 TeV.

Journal of High Energy Physics, 2010

We analyse a family of brane-world black holes which solve the effective four-dimensional Einstei... more We analyse a family of brane-world black holes which solve the effective four-dimensional Einstein equations for a wide range of parameters related to the unknown bulk/brane physics. We first constrain the parameters using known experimental bounds and, for the allowed cases, perform a numerical analysis of their time evolution, which includes accretion through the Earth. The study is aimed at

The minimal geometric deformation approach is employed to show the existence of braneworld stella... more The minimal geometric deformation approach is employed to show the existence of braneworld stellar distributions with vacuum Schwarzschild exterior, thus without energy leaking from the exterior of the brane-world star into the extra dimension. The interior satisfies all elementary criteria of physical acceptability for a stellar solution, namely, it is regular at the origin, the pressure and density are positive and decrease monotonically with increasing radius, finally all energy conditions are fulfilled. A very thin solid crust with negative radial pressure separates the interior from the exterior, having a thickness ∆ inversely proportional to both the brane tension σ and the radius R of the star, i.e. ∆ −1 ∼ R σ. This brane-world star with Schwarzschild exterior would appear only thermally radiating to a distant observer and be fully compatible with the stringent constraints imposed on stellar parameters by observations of gravitational lensing, orbital evolutions or properties of accretion disks. * jovalle@usb.ve † laszlo.a.

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking tempera... more We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

A localised particle in Quantum Mechanics is described by a wave packet in position space, regard... more A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.

Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investi... more Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.

International Journal of Modern Physics D, 2009

It has recently been debated whether a class of generalized uncertainty principles that include g... more It has recently been debated whether a class of generalized uncertainty principles that include gravitational sources of error is compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the

Quantum Aspects of Black Holes, 2014

We review the main consequences of the possible existence of a minimum measurable length, of the ... more We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures.