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Register a new userDirac equation for sphercially symmetric $AdS_5$ space-time and application to a boson star in EGB gravity
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We discuss the Dirac equation in a curved 5-dimensional spherically symmetric space-time. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating space-times with equal angular momenta. It has a symmetry $SU(2)times U(1)$ and is implemented by the Wigner functions. The radial part forms a Dirac-Schrodinger type equation, and existence of the analytical solutions of the massless and the massive modes is confirmed. The solutions are described by the Jacobi polynomials. Also, the spinor of the both large and small components is obtained numerically. As a direct application of our formulation, we evaluate the spectrum of the Dirac fermion in Einstein-Gauss-Bonnet space-time and the space-time of a boson star.
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Relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry is considered. The Fermi coordinates adapted to the time-like geodesic are utilized to describe the low-energy physics in the laboratory and to calculate the leading correction due to the curvature of the space-time geometry to the Schrodinger equation. The correction is employed to calculate the probability of excitation for a hydrogen atom that falls in or is scattered by a general Schwarzchild black hole. Since the excited states decay due to spontaneous photon emission, this study provides the theoretical base for detection of small isolated black holes by observing the decay of the excited states as neutral hydrogen atoms in the vacuum are devoured by the black hole.
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We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($dgeqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the assumptions made, this conformally invariant wave operator is unique. The corresponding conformally invariant wave equation can be obtained from a Lagrangian which is explicitly given. We discuss how our result compares to previous works, in particular we hope to clarify the situation between conflicting results.
In this paper we perform a full gauge-fixing of the phase space of four dimensional General Relativity (GR) of Lorentzian signature for the time symmetric case, using the CDJ variables. In particular, the Gauss law constraint in the chosen gauge meets the conditions of the Cauchy-Kovalevskaya theorem for first order, quasilinear PDEs. This implies the existence of a unique analytic solution to the initial value constraints problem in some region of 3-space, featuring four free functions per spacetime point. This result constitutes a step toward addressal of the reduced phase space problem of GR.
Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energys level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p,c^2$, and a B-H temperature: $T_{BH}=left(frac{hbar,c}{2pi,l_p,K_B}right)$.
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