Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStress-Energy in the Conical Vacuum and its Implications for Topology Change
91
0
0.0
(
0
)
Authors
Eric B. Jones
Ask ChatGPT about the research
No Arabic abstract
This dissertation presents a semiclassical analysis of conical topology change in $1+1$ spacetime dimensions wherein, to lowest order, the ambient spacetime is classical and fixed while the scalar field coupled to it is quantized. The vacuum expectation value of the scalar field stress-energy tensor is calculated via two different approaches. The first of these involves the explicit determination of the so called Sorkin-Johnston state on the cone and an original regularization scheme, while the latter employs the conformal vacuum and the more conventional point-splitting renormalization. It is found that conical topology change seems not to suffer from the same pathologies that trousers-type topology change does. This provides tentative agreement with conjectures due to Sorkin and Borde, which attempt to classify topology changing spacetimes with respect to their Morse critical points and in particular, that the cone and yarmulke in $1+1$ dimensions lack critical points of unit Morse index.
rate research
Read More
Semiclassical Physics in gravitational scenario, in its first approximation (1st order) cares only for the expectation value of stress energy tensor and ignores the inherent quantum fluctuations thereof. In the approach of stochastic gravity, on the other hand, these matter fluctuations are supposed to work as the source of geometry fluctuations and have the potential to render the results from 1st order semiclassical physics irrelevant. We study the object of central significance in stochastic gravity, i.e. the noise kernel, for a wide class of Friedmann space-times. Through an equivalence of quantum fields on de Sitter space-time and those on generic Friedmann universes, we obtain the noise kernel through the correlators of Stress Energy Tensor (SET) for fixed co-moving but large physical distances. We show that in many Friedmann universes including the expanding universes, the initial quantum fluctuations, the universe is born with, may remain invariant and important even at late times. Further, we explore the cosmological space-times where even after long times the quantum fluctuations remain strong and become dominant over large physical distances, which the matter driven universe is an example of. The study is carried out in minimal as well as non-minimal interaction settings. Implications of such quantum fluctuations are discussed.
We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. So far we developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally-coupled massless scalar field in Schwarzschild and Reissner-Nordstrom backgrounds, for several quantum states. We present here the results for the RSET in the Schwarzschild case in Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at $rlesssim2.78M$. Then we use the RSET results to explore violation of the weak and null Energy conditions. We find that both conditions are violated all the way from $rsimeq4.9M$ to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at $r=3M$ violates the averaged null energy condition.
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor for idealized boundary conditions with some finite cutoff should be a reasonable ad hoc model for the true situation. The theory will have a sensible renormalized limit when the cutoff is taken away; this requires making sense of the Einstein equation with a distributional source. Calculations with the standard ultraviolet cutoff reveal an inconsistency between energy and pressure similar to the one that arises in noncovariant regularizations of cosmological vacuum energy. The problem disappears, however, if the cutoff is a spatial point separation in a neutral direction parallel to the boundary. Here we demonstrate these claims in detail, first for a single flat reflecting wall intersected by a test boundary, then more rigorously for a region of finite cross section surrounded by four reflecting walls. We also show how the moment-expansion theorem can be applied to the distributional limits of the source and the solution of the Einstein equation, resulting in a mathematically consistent differential equation where cutoff-dependent coefficients have been identified as renormalizations of properties of the boundary. A number of issues surrounding the interpretation of these results are aired.
Archimedes is a feasibility study to a future experiment to ascertain the interaction of vacuum fluctuations with gravity. The future experiment should measure the force that the Earths gravitational field exerts on a Casimir cavity by using a balance as the small force detector. The Archimedes experiment analyses the important parameters in view of the final measurement and experimentally explores solutions to the most critical problems.
In this paper the Feynman Green function for Maxwells theory in curved space-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
