Robert B. Mann

Hilbert space representation of the minimal length uncertainty relation

The existence of a minimal observable length has long been suggested in quantum gravity as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation. DAMTP/94-105, hep-th/9412167, and Phys.Rev.D52:1108 (1995)

P − V criticality of charged AdS black holes

A bstractTreating the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the critical behaviour of charged AdS black holes. We complete the analogy of this system with the liquid-gas system and study its critical point, which occurs at the point of divergence of specific heat at constant pressure. We calculate the critical exponents and show that they coincide with those of the Van der Waals system.

Tunnelling, temperature, and Taub-NUT black holes

We investigate quantum tunnelling methods for calculating black hole temperature, specifically the null-geodesic method of Parikh and Wilczek and the Hamilton-Jacobi Ansatz method of Angheben et al. We consider application of these methods to a broad class of spacetimes with event horizons, including Rindler and nonstatic spacetimes such as Kerr-Newman and Taub-NUT. We obtain a general form for the temperature of Taub-NUT-AdS black holes that is commensurate with other methods. We examine the limitations of these methods for extremal black holes, taking the extremal Reissner-Nordstrom spacetime as a case in point.

Fermions tunnelling from black holes

We investigate the tunnelling of spin-1/2 particles through event horizons. We first apply the tunnelling method to Rindler spacetime and obtain the Unruh temperature. We then apply fermion tunnelling to a general non-rotating black hole metric and show that the Hawking temperature is recovered.

Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization

A bstractWe investigate the critical behaviour of charged and rotating AdS black holes in d spacetime dimensions, including effects from non-linear electrodynamics via the Born-Infeld action, in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure. For Reissner-Nördstrom black holes we find that the analogy with the Van der Walls liquid-gas system holds in any dimension greater than three, and that the critical exponents coincide with those of the Van der Waals system. We find that neutral slowly rotating black holes in four space-time dimensions also have the same qualitative behaviour. However charged and rotating black holes in three spacetime dimensions do not exhibit critical phenomena. For Born-Infeld black holes we define a new thermodynamic quantity B conjugate to the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We demonstrate that this quantity is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.

Charged Fermions Tunnelling from Kerr-Newman Black Holes

Abstract We consider the tunnelling of charged spin 1/2 fermions from a Kerr–Newman black hole and demonstrate that the expected Hawking temperature is recovered. We discuss certain technical subtleties related to the obtention of this result.

Pair production of topological anti-de Sitter black holes

The pair creation of black holes with event horizons of non-trivial topology is described. The spacetimes are all limiting cases of the cosmological C-metric. They are generalizations of the (2 + 1)-dimensional black hole and have asymptotically anti-de Sitter behaviour. Domain wall instantons can mediate their pair creation for a wide range of mass and charge.

Alice Falls into a Black Hole: Entanglement in Noninertial Frames

Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in noninertial frames. In the high acceleration limit, our results can be applied to a nonaccelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the states distillable entanglement vanishes.

Temperature, energy, and heat capacity of asymptotically anti-de Sitter black holes.

We investigate the thermodynamical properties of black holes in (3+1)- and (2+1)-dimensional Einstein gravity with a negative cosmological constant. In each case, ther thermodynamic internal energy is computed for a finite spatial region that contains the black hole. The temperature at the boundary of this regoin is defined by differentiating the energy with respect to entropy, and is equal to the product of the surface gravity (divided by 2\ensuremath{\pi}) and the Tolman redshift factor for temperature in a stationary gravitational field. We also compute the thermodynamic surface pressure and, in the case of the 2+1 black hole, show that the chemical potential conjugate to angular momentum is equal to the proper angular velocity of the black hole with respect to observers who are at rest in the stationary time slices. In 3+1 dimensions, a calculation of the heat capacity reveals the existence of a thermodynamically stable black hole solution and a negative heat capacity instanton. This result holds in the limit that the spatial boundary tends to infinity only if the cosmological constant is negative; if the cosmological constant vanishes, the stable black hole solution is lost. In 2+1 dimensions, a calculation of the heat capacity reveals the existence of a thermodynamically stable black hole solution, but no negative heat capacity instanton.

Entanglement of Dirac fields in noninertial frames

We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a nonvanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multiqubit complementarity.