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Papers by Robert Penna
Monthly Notices of the Royal Astronomical Society, 2014
2013 IEEE International Symposium on Phased Array Systems and Technology, 2013
The Astrophysical Journal, 2012
Physical Review D, 2014
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are ent... more If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER ¼ EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and Cadney-Linden-Winter inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER ¼ EPR. We further show that the entanglement entropy associated with classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state jGHZ 4 i ¼ ðj0000i þ j1111iÞ= ffiffi ffi 2 p has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of jGHZ 4 i states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.
Monthly Notices of the Royal Astronomical Society, 2011
We present an analytical solution for thin-disc accretion on to a Kerr black hole that extends th... more We present an analytical solution for thin-disc accretion on to a Kerr black hole that extends the standard Novikov-Thorne α-disc in three ways: (i) it incorporates non-zero stresses at the inner edge of the disc; (ii) it extends into the plunging region; and (iii) it uses a corrected vertical gravity formula. The free parameters of the model are unchanged. Non-zero boundary stresses are included by replacing the Novikov-Thorne no-torque boundary condition with the less strict requirement that the fluid velocity at the innermost stable circular orbit is the sound speed, which numerical models show to be the correct behaviour for luminosities below ∼30 per cent Eddington. We assume the disc is thin so we can ignore advection. Boundary stresses scale as αh and advection terms scale as h 2 [where h is the disc opening angle (h = H/r)], so the model is self-consistent when h < α. We compare our solution with slim-disc models and general relativistic magnetohydrodynamic disc simulations. The model may improve the accuracy of black hole spin measurements.
Monthly Notices of the Royal Astronomical Society, 2013
Using long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficie... more Using long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficient accretion discs, the energy, momentum and mass outflow rates from such systems are estimated. Outflows occur via two fairly distinct modes: a relativistic jet and a subrelativistic wind. The jet power depends strongly on the black hole spin and on the magnetic flux at the horizon. Unless these are very small, the energy output in the jet dominates over that in the wind. For a rapidly spinning black hole accreting in the magnetically arrested limit, it is confirmed that jet power exceeds the total rate of accretion of rest mass energy. However, because of strong collimation, the jet probably does not have a significant feedback effect on its immediate surroundings. The power in the wind is more modest and shows a weaker dependence on black hole spin and magnetic flux. Nevertheless, because the wind subtends a large solid angle, it is expected to provide efficient feedback on a wide range of scales inside the host galaxy. Empirical formulae are obtained for the energy and momentum outflow rates in the jet and the wind.
Monthly Notices of the Royal Astronomical Society, 2011
The X-ray spectra of accretion discs of eight stellar mass black holes have been analysed to date... more The X-ray spectra of accretion discs of eight stellar mass black holes have been analysed to date using the thermal continuum-fitting method, and the spectral fits have been used to estimate the spin parameters of the black holes. However, the underlying model used in this method of estimating spin is the general relativistic thin-disc model of Novikov & Thorne, which is only valid for razor-thin discs. We therefore expect errors in the measured values of spin due to inadequacies in the theoretical model. We investigate this issue by computing spectra of numerically calculated models of thin accretion discs around black holes, obtained via three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. We apply the continuum-fitting method to these computed spectra to estimate the black hole spins and check how closely the values match the actual spin used in the GRMHD simulations. We find that the error in the dimensionless spin parameter is up to about 0.2 for a non-spinning black hole, depending on the inclination. For black holes with spins of 0.7, 0.9 and 0.98, the errors are up to about 0.1, 0.03 and 0.01, respectively. These errors are comparable to or smaller than those arising from current levels of observational uncertainty. Furthermore, we estimate that the GRMHD simulated discs from which these error estimates are obtained correspond to effective disc luminosities of about 0.4-0.7 Eddington, and that the errors will be smaller for discs with luminosities of 0.3 Eddington or less, which are used in the continuum-fitting method. We thus conclude that use of the Novikov-Thorne thin-disc model does not presently limit the accuracy of the continuum-fitting method of measuring black hole spin.
Monthly Notices of the Royal Astronomical Society, 2010
The standard general relativistic model of a razor-thin accretion disc around a black hole, devel... more The standard general relativistic model of a razor-thin accretion disc around a black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear stress vanishes at the radius of the innermost stable circular orbit (ISCO) and that, outside the ISCO, the shear stress is produced by an effective turbulent viscosity. However, astrophysical accretion discs are not razor thin; it is uncertain whether the shear stress necessarily vanishes at the ISCO, and the magnetic field, which is thought to drive turbulence in discs, may contain large-scale structures that do not behave like a simple local scalar viscosity. We describe 3D general relativistic magnetohydrodynamic simulations of accretion discs around black holes with a range of spin parameters, and we use the simulations to assess the validity of the NT model. Our fiducial initial magnetic field consists of multiple (alternating polarity) poloidal field loops whose shape is roughly isotropic in the disc in order to match the isotropic turbulence expected in the poloidal plane. For a thin disc with an aspect ratio |h/r| ∼ 0.07 around a non-spinning black hole, we find a decrease in the accreted specific angular momentum of 2.9 per cent relative to the NT model and an excess luminosity from inside the ISCO of 3.5 per cent. The deviations in the case of spinning black holes are also of the same order. In addition, the deviations decrease with decreasing |h/r|. We therefore conclude that magnetized thin accretion discs in X-ray binaries in the thermal/high-soft spectral state ought to be well described by the NT model, especially at luminosities below 30 per cent of Eddington where we expect a very small disc thickness |h/r| 0.05. We use our results to determine the spin equilibrium of black hole accretion discs with a range of thicknesses and to determine how electromagnetic stresses within the ISCO depend upon black hole spin and disc thickness. We find that the electromagnetic stress and the luminosity inside the ISCO depend on the assumed initial magnetic field geometry. We consider a second geometry with field lines following density contours, which for thin discs leads to highly radially elongated magnetic field lines. This gives roughly twice larger deviations from NT for both the accreted specific angular momentum and the luminosity inside the ISCO. Lastly, we find that the disc's corona (including any wind or jet) introduces deviations from NT in the specific angular momentum that are comparable to those contributed by the disc component, while the excess luminosity of bound gas from within the ISCO is dominated by only the disc component. Based on these indications, we suggest that differences in results between our work and other similar work are due to differences in the assumed initial magnetic field geometry as well as the inclusion of disc
Classical and Quantum Gravity, 2011
Journal of Mathematical Physics, 2020
The group of area preserving diffeomorphisms of the two sphere, SDiff(S2), is one of the simplest... more The group of area preserving diffeomorphisms of the two sphere, SDiff(S2), is one of the simplest examples of an infinite dimensional Lie group. It plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related, newly defined symmetry groups. We investigate its representation theory using the method of coadjoint orbits. We describe the Casimir functions and the Cartan algebra. Then we evaluate the trace of a simple SDiff(S2) operator using the Atiyah-Bott fixed point formula. The trace is divergent but we show that it has well-defined truncations related to the structure of SDiff(S2). Finally, we relate our results back to the recent appearances of SDiff(S2) in black hole physics.
Monthly Notices of the Royal Astronomical Society, 2014
2013 IEEE International Symposium on Phased Array Systems and Technology, 2013
The Astrophysical Journal, 2012
Physical Review D, 2014
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are ent... more If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER ¼ EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and Cadney-Linden-Winter inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER ¼ EPR. We further show that the entanglement entropy associated with classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state jGHZ 4 i ¼ ðj0000i þ j1111iÞ= ffiffi ffi 2 p has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of jGHZ 4 i states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.
Monthly Notices of the Royal Astronomical Society, 2011
We present an analytical solution for thin-disc accretion on to a Kerr black hole that extends th... more We present an analytical solution for thin-disc accretion on to a Kerr black hole that extends the standard Novikov-Thorne α-disc in three ways: (i) it incorporates non-zero stresses at the inner edge of the disc; (ii) it extends into the plunging region; and (iii) it uses a corrected vertical gravity formula. The free parameters of the model are unchanged. Non-zero boundary stresses are included by replacing the Novikov-Thorne no-torque boundary condition with the less strict requirement that the fluid velocity at the innermost stable circular orbit is the sound speed, which numerical models show to be the correct behaviour for luminosities below ∼30 per cent Eddington. We assume the disc is thin so we can ignore advection. Boundary stresses scale as αh and advection terms scale as h 2 [where h is the disc opening angle (h = H/r)], so the model is self-consistent when h < α. We compare our solution with slim-disc models and general relativistic magnetohydrodynamic disc simulations. The model may improve the accuracy of black hole spin measurements.
Monthly Notices of the Royal Astronomical Society, 2013
Using long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficie... more Using long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficient accretion discs, the energy, momentum and mass outflow rates from such systems are estimated. Outflows occur via two fairly distinct modes: a relativistic jet and a subrelativistic wind. The jet power depends strongly on the black hole spin and on the magnetic flux at the horizon. Unless these are very small, the energy output in the jet dominates over that in the wind. For a rapidly spinning black hole accreting in the magnetically arrested limit, it is confirmed that jet power exceeds the total rate of accretion of rest mass energy. However, because of strong collimation, the jet probably does not have a significant feedback effect on its immediate surroundings. The power in the wind is more modest and shows a weaker dependence on black hole spin and magnetic flux. Nevertheless, because the wind subtends a large solid angle, it is expected to provide efficient feedback on a wide range of scales inside the host galaxy. Empirical formulae are obtained for the energy and momentum outflow rates in the jet and the wind.
Monthly Notices of the Royal Astronomical Society, 2011
The X-ray spectra of accretion discs of eight stellar mass black holes have been analysed to date... more The X-ray spectra of accretion discs of eight stellar mass black holes have been analysed to date using the thermal continuum-fitting method, and the spectral fits have been used to estimate the spin parameters of the black holes. However, the underlying model used in this method of estimating spin is the general relativistic thin-disc model of Novikov & Thorne, which is only valid for razor-thin discs. We therefore expect errors in the measured values of spin due to inadequacies in the theoretical model. We investigate this issue by computing spectra of numerically calculated models of thin accretion discs around black holes, obtained via three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. We apply the continuum-fitting method to these computed spectra to estimate the black hole spins and check how closely the values match the actual spin used in the GRMHD simulations. We find that the error in the dimensionless spin parameter is up to about 0.2 for a non-spinning black hole, depending on the inclination. For black holes with spins of 0.7, 0.9 and 0.98, the errors are up to about 0.1, 0.03 and 0.01, respectively. These errors are comparable to or smaller than those arising from current levels of observational uncertainty. Furthermore, we estimate that the GRMHD simulated discs from which these error estimates are obtained correspond to effective disc luminosities of about 0.4-0.7 Eddington, and that the errors will be smaller for discs with luminosities of 0.3 Eddington or less, which are used in the continuum-fitting method. We thus conclude that use of the Novikov-Thorne thin-disc model does not presently limit the accuracy of the continuum-fitting method of measuring black hole spin.
Monthly Notices of the Royal Astronomical Society, 2010
The standard general relativistic model of a razor-thin accretion disc around a black hole, devel... more The standard general relativistic model of a razor-thin accretion disc around a black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear stress vanishes at the radius of the innermost stable circular orbit (ISCO) and that, outside the ISCO, the shear stress is produced by an effective turbulent viscosity. However, astrophysical accretion discs are not razor thin; it is uncertain whether the shear stress necessarily vanishes at the ISCO, and the magnetic field, which is thought to drive turbulence in discs, may contain large-scale structures that do not behave like a simple local scalar viscosity. We describe 3D general relativistic magnetohydrodynamic simulations of accretion discs around black holes with a range of spin parameters, and we use the simulations to assess the validity of the NT model. Our fiducial initial magnetic field consists of multiple (alternating polarity) poloidal field loops whose shape is roughly isotropic in the disc in order to match the isotropic turbulence expected in the poloidal plane. For a thin disc with an aspect ratio |h/r| ∼ 0.07 around a non-spinning black hole, we find a decrease in the accreted specific angular momentum of 2.9 per cent relative to the NT model and an excess luminosity from inside the ISCO of 3.5 per cent. The deviations in the case of spinning black holes are also of the same order. In addition, the deviations decrease with decreasing |h/r|. We therefore conclude that magnetized thin accretion discs in X-ray binaries in the thermal/high-soft spectral state ought to be well described by the NT model, especially at luminosities below 30 per cent of Eddington where we expect a very small disc thickness |h/r| 0.05. We use our results to determine the spin equilibrium of black hole accretion discs with a range of thicknesses and to determine how electromagnetic stresses within the ISCO depend upon black hole spin and disc thickness. We find that the electromagnetic stress and the luminosity inside the ISCO depend on the assumed initial magnetic field geometry. We consider a second geometry with field lines following density contours, which for thin discs leads to highly radially elongated magnetic field lines. This gives roughly twice larger deviations from NT for both the accreted specific angular momentum and the luminosity inside the ISCO. Lastly, we find that the disc's corona (including any wind or jet) introduces deviations from NT in the specific angular momentum that are comparable to those contributed by the disc component, while the excess luminosity of bound gas from within the ISCO is dominated by only the disc component. Based on these indications, we suggest that differences in results between our work and other similar work are due to differences in the assumed initial magnetic field geometry as well as the inclusion of disc
Classical and Quantum Gravity, 2011
Journal of Mathematical Physics, 2020
The group of area preserving diffeomorphisms of the two sphere, SDiff(S2), is one of the simplest... more The group of area preserving diffeomorphisms of the two sphere, SDiff(S2), is one of the simplest examples of an infinite dimensional Lie group. It plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related, newly defined symmetry groups. We investigate its representation theory using the method of coadjoint orbits. We describe the Casimir functions and the Cartan algebra. Then we evaluate the trace of a simple SDiff(S2) operator using the Atiyah-Bott fixed point formula. The trace is divergent but we show that it has well-defined truncations related to the structure of SDiff(S2). Finally, we relate our results back to the recent appearances of SDiff(S2) in black hole physics.