Gabriel Abreu, PhD Student

Please Note

This person can no longer be contacted through the School of Mathematics, Statistics and Operations Research at Victoria University of Wellington

Articles

• Quantum Interest in (3+1) dimensional Minkowski space

  Authors: Gabriel Abreu (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)
  http://arxiv.org/abs/0808.1931

  Abstract: The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially preventing the existence of exotic phenomena such as "Alcubierre warp-drives" or "traversable wormholes". Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.

• Kodama time

  Authors: Gabriel Abreu (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)

  http://arxiv.org/abs/1004.1456

  Abstract: In a general time-dependent (3+1)-dimensional spherically symmetric spacetime, the so-called Kodama vector is a naturally defined geometric quantity that is timelike outside the evolving horizon and so defines a preferred class of fiducial observers. However the Kodama vector does not by itself define any preferred notion of time. We demonstrate that a preferred time coordinate - which we shall call Kodama time - can be introduced by taking the additional step of applying the Clebsch decomposition theorem to the Kodama vector. We thus construct a geometrically preferred coordinate system for any time-dependent spherically symmetric spacetime, and explore its properties. In particular we use this formalism to construct a general class of conservation laws, generalizing Kodama's energy flux. We study the geometrically preferred fiducial observers, and demonstrate that it is possible to define and calculate a generalized notion of surface gravity that is valid throughout the entire evolving spacetime. Furthermore, by building and suitably normalizing set of radial null geodesics, we can show that this generalized surface gravity passes several consistency tests and has a physically appropriate static limit.

• Tolman mass, generalized surface gravity, and entropy bounds

  Authors: Gabriel Abreu (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)

  http://arxiv.org/abs/1005.1132

  Abstract: In any static spacetime the quasi-local Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics and invoking the Unruh effect one can then develop elementary bounds on the quasi-local entropy that are very similar in spirit to the holographic bound, and closely related to entanglement entropy.