In this work, we have continued the study of the Hawking radiation on the brane from a higher-dimensional rotating black hole by investigating the emission of fermionic modes. A comprehensive analysis is performed that leads to the particle, power and angular momentum emission rates, and sheds light on their dependence on fundamental parameters of the theory, such as the spacetime dimension and angular momentum of the black hole. In addition, the angular distribution of the emitted modes, in terms of the number of particles and energy, is thoroughly studied. Our results are valid for arbitrary values of the energy of the emitted particles, dimension of spacetime and angular momentum of the black hole, and complement previous results on the emission of brane-localised scalars and gauge bosons.

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Brane decay of a (4+n)-dimensional rotating black hole. III: spin-1/2 particles

The low energy effective action of gravity in any even dimension generally acquires nonlocal terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of the gravitational field. The scalar potentials also provide coordinate invariant order parameters describing the conformal behavior and divergences of the stress tensor on event horizons. We compute the stress tensor due to the anomaly in terms of its auxiliary scalar potentials in a number of concrete examples, including the Rindler wedge, the Schwarzschild geometry, and de Sitter spacetime. In all of these cases, a small number of classical order parameters completely determine the divergent behaviors allowed on the horizon, and yield qualitatively correct global approximations to the renormalized expectation value of the quantum stress tensor.

Macroscopic effects of the quantum trace anomaly

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordstrom black holes. They also possess a finite mass M and electric charge Qe, with Qe/M>1. An exact wormhole solution with ungauged, massless fermions is also reported.

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Traversable Wormholes in Einstein-Dirac-Maxwell Theory

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Brane Decay of a (4+n)-Dimensional Rotating Black Hole. III: spin-1/2 particles

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Macroscopic Effects of the Quantum Trace Anomaly

A method for computing the stress-energy tensor for the quantized, massless, spin $\frac{1}{2}$ field in a general static spherically symmetric spacetime is presented. The field can be in a zero temperature state or a nonzero temperature thermal state. An expression for the full renormalized stress-energy tensor is derived. It consists of a sum of two tensors both of which are conserved. One tensor is written in terms of the modes of the quantized field and has zero trace. In most cases it must be computed numerically. The other tensor does not explicitly depend on the modes and has a trace equal to the trace anomaly. It can be used as an analytic approximation for the stress-energy tensor and is equivalent to other approximations that have been made for the stress-energy tensor of the massless spin $\frac{1}{2}$ field in static spherically symmetric spacetimes.

Method to compute the stress-energy tensor for the massless spin 1 2 field in a general static spherically symmetric spacetime

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static nonrotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom, and extreme Reissner-Nordstrom solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.

Peter B. Groves

Papers

Method to compute the stress-energy tensor for the massless spin 1 2 field in a general static spherically symmetric spacetime

Stress-energy tensor for a massless spin 1/2 field in static black hole spacetimes