M.Sc Student | Lanir Assaf |
---|---|

Subject | Computation of a Scalar-Field Squared Expectation Value Inside 4-Dimensional Schwarzschild and Reissner-Nordstrom Black Holes |

Department | Department of Physics |

Supervisor | Professor Amos Ori |

Full Thesis text |

The discovery that the classical theory of general relativity admits black hole (BH) solutions led eventually to the study of their internal structure. Endowed with remarkable features, such as Cauchy horizons, bridges between universes, closed time-like curves and naked singularities, BH interiors proved to be an extraordinarily interesting fertile ground for understanding the large scale structure of spacetime.

BHs had yet
more in store for us, as realized when quantum effects had begun to be taken
into account within the framework of semiclassical general relativity.
Particularly, BH evaporation through the emission ofHawking radiation poses the
questions of the fate of the evaporating BH and the information therein (a
problem known as the “information loss puzzle”). Clearly, quantum effects
change considerably the internal structure of BHs, and a straightforward way to
investigate the resulting picture within the semiclassical framework is to
compute the renormalized stress-energy tensor (RSET) in 4D BH interiors. In
this thesis, we make a first step towards that goal and compute the
renormalized expectation value of *<Φ*^{2}(*x*) *>
*for a minimally-coupled, massless scalar field in the interior of 4D
Schwarzschild and Reissner-Nordström (RN) BHs.

The full
computation of the renormalized expectation values *<Φ*^{2}(*x*)
*>* and the RSET* *in 4D BH interiors has been a long standing
challenge, which has impeded the investigation of quantum effects on the
internal structure of BHs for decades. Employing a recently developed mode sum
renormalization scheme to numerically implement the point-splitting method, we
report here the first computation of *<Φ*^{2}(*x*)*> _{ren}*
in Unruh state in the region interior to the event horizon of a 4D
Schwarzschild BH. We further present its Hartle-Hawking counterpart, which we
calculated using the same method, and obtain a fairly good agreement with
previous results attained using an entirely different method by Candelas and Jensen
in 1986. Our results further agree upon approaching the event horizon when compared
with previous results calculated outside the BH.

We further
report here the first computation of *<Φ*^{2}(*x*)*> _{ren}*
in both Hartle-Hawking and Unruh states inside a 4D RN BH. Our results agree at
the external event horizon with those previously obtained outside the event
horizon (A. Levi and A. Ori) and with analytic asymptotic approximations (A.
Ottewill). They also agree with our results obtained by a semi-asymptotic
approximation at the vicinity of the inner (Cauchy) horizon. Finally, our
results are consistent with those of an asymptotic analysis of the expected
leading order in

This work sets
the stage for further explorations of *<Φ*^{2}(*x*)*> _{ren}*
and the RSET