Tunneling between single and multi-centered black hole configurations

We find a gravitational instanton that connects an initial state corresponding to a single-centered extremal Reissner-Nordstrom (ERN) black hole configuration, to a final state corresponding to a multi-centered configuration. This instanton is interpreted as describing quantum tunneling between the two different black hole solutions. We evaluate the Euclidean action for this instanton and find that the amplitude for the tunneling process is equal to half the difference in entropy between the initial and final configurations.Comment: 8 pages, 4 figures. v4: final version accepted for publication in Phys. Rev.

Asymptotic Symmetries of Rindler Space at the Horizon and Null Infinity

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.Comment: 37 pages, 4 figures. Version 3: New Section 5 adde

Exploring Black Hole Dynamics

This thesis explores the evolution of different types of black holes, and the ways in which black hole dynamics can be used to answer questions about other physical systems. We first investigate the differences in observable gravitational effects between a four-dimensional Randall-Sundrum (RS) braneworld universe compared to a universe without the extra dimension, by considering a black hole solution to the braneworld model that is localized on the brane. When the brane has a negative cosmological constant, then for a certain range of parameters for the black hole, the intersection of the black hole with the brane approximates a Banados-Teitelboim-Zanelli (BTZ) black hole on the brane with corrections that fall off exponentially outside the horizon. We compute the quasinormal modes of the braneworld black hole, and compare them to the known quasinormal modes of the three-dimensional BTZ black hole. We find that there are two distinct regions for the braneworld black hole solutions that are reflected in the dependence of the quasinormal modes on the black hole mass. The imaginary parts of the quasinormal modes display phenomenological similarities to the quasinormal modes of the three-dimensional BTZ black hole, indicating that nonlinear gravitational effects may not be enough to distinguish between a lower-dimensional theory and a theory derived from a higher-dimensional braneworld. Secondly, we consider the evolution of non-extremal black holes in N=4, d=2 supergravity, and investigate how such black holes might evolve over time if perturbed away from extremality. We study this problem in the probe limit by finding tunneling amplitudes for a Dirac field in a single-centered background, which gives the decay rates for the emission of charged probe black holes from the central black hole. We find that there is no minimum to the potential for the probe particles at a finite distance from the central black hole, so any probes that are emitted escape to infinity. If the central black hole is BPS in the extremal limit, then the potential is flat and so there is no barrier to the emission of probes. If the central black hole is non-BPS in the extremal limit, then there is a barrier to emission and we compute the decay rate, which depends both on the charge of the central black hole and the charges of the emitted black holes. Finally, we consider the possibility that an extremal black hole, the end-point of the evolution of a non-extremal black hole through evaporation, may itself split into a multi-centered black hole solution through quantum tunneling, via a gravitational instanton analogous to the instanton for the symmetric double well in elementary quantum mechanics. We find a gravitational instanton that connects two vacuum states: one state corresponding to a single-centered extremal Reissner-Nordstrom (ERN) black hole configuration, and another state corresponding to a multi-centered ERN configuration. We evaluate the Euclidean action for this instanton and find that the amplitude for the tunneling process is equal to half the difference in entropy between the initial and final configurations

Local unitary versus local Clifford equivalence of stabilizer and graph states

The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [Phys. Rev. \textbf{A71}, 062323]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence ($LU\Leftrightarrow LC$) to include all stabilizer states represented by graphs with neither cycles of length 3 nor 4. To compare our result with Van den Nest et al.'s, we show that any stabilizer state of distance $\delta=2$ is beyond their criterion. We then further prove that $LU\Leftrightarrow LC$ holds for a more general class of stabilizer states of $\delta=2$. We also explicitly construct graphs representing $\delta>2$ stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with $2^m-1$ ($m\geq 4$) vertices using quantum error correcting codes which have non-Clifford transversal gates.Comment: Revised version according to referee's comments. To appear in Physical Review