Spectral action and the electroweak θ-terms for the Standard Model without fermion doubling

We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological θ-terms for the electroweak gauge fields.

Black Hole Radiation, Greybody Factors, and Generalised Wick Rotation

<p>In this thesis we look at the intersection of quantum field theory and general relativity. We focus on Hawking radiation from black holes and its implications. This is done on two fronts. In the first we consider the greybody factors arising from a Schwarzschild black hole. We develop a new way to numerically calculate these greybody factors using the transfer matrix formalism and the product calculus. We use this technique to calculate some of the relevant physical quantities and consider their effect on the radiation process. The second front considers a generalisation of Wick rotation. This is motivated by the success of Wick rotation and Euclidean quantum field theory techniques to calculate the Hawking temperature. We find that, while an analytic continuation of the coordinates is not well defined and highly coordinate dependent, a direct continuation of the Lorentzian signature metric to Euclidean signature has promising results. It reproduces the Hawking temperature and is coordinate independent. However for consistency, we propose a new action for the Euclidean theory which cannot be simply the Euclidean Einstein-Hilbert action.</p>

Black Hole Radiation, Greybody Factors, and Generalised Wick Rotation

<p>In this thesis we look at the intersection of quantum field theory and general relativity. We focus on Hawking radiation from black holes and its implications. This is done on two fronts. In the first we consider the greybody factors arising from a Schwarzschild black hole. We develop a new way to numerically calculate these greybody factors using the transfer matrix formalism and the product calculus. We use this technique to calculate some of the relevant physical quantities and consider their effect on the radiation process. The second front considers a generalisation of Wick rotation. This is motivated by the success of Wick rotation and Euclidean quantum field theory techniques to calculate the Hawking temperature. We find that, while an analytic continuation of the coordinates is not well defined and highly coordinate dependent, a direct continuation of the Lorentzian signature metric to Euclidean signature has promising results. It reproduces the Hawking temperature and is coordinate independent. However for consistency, we propose a new action for the Euclidean theory which cannot be simply the Euclidean Einstein-Hilbert action.</p>

Supersymmetric black holes with spiky horizons

We use the recipe of [1] to find half-BPS near-horizon geometries in the t3 model of N = 2, D = 4 gauged supergravity, and explicitely construct some new examples. Among these are black holes with noncompact horizons, but also with spherical horizons that have conical singularities (spikes) at one of the two poles. A particular family of them is extended to the full black hole geometry. Applying a double-Wick rotation to the near-horizon region, we obtain solutions with NUT charge that asymptote to curved domain walls with AdS3 world volume. These new solutions may provide interesting testgrounds to address fundamental questions related to quantum gravity and holography.

Accretion Flow onto Ellis–Bronnikov Wormhole

Study of accretion onto wormholes is rather rare compared to that onto black holes. In this paper, we consider accretion flow of cosmological dark energy modeled by barotropic fluid onto the celebrated Ellis–Bronnikov wormhole (EBWH) built by Einstein minimally coupled scalar field ϕ, violating the null energy condition. The accreting fluid is assumed to be phantom, quintessence, dust and stiff matter. We begin by first pointing out a mathematical novelty showing how the EBWH can lead to the Schwarzschild black hole under a complex Wick rotation. Then, we analyze the profiles of fluid radial velocity, density and the rate of mass variation of the EBWH due to accretion and compare the profiles with those of the Schwarzschild black hole. We also analyze accretion to the massless EBWH that has zero ADM mass but has what we call nonzero Wheelerian mass (“mass without mass”), composed of the non-trivial scalar field, that shows gravitational effects. Our conclusion is that the mass of SBH due to phantom accretion decreases consistently with known results, while, in contrast, the mass of EBWH increases. Exactly an opposite behavior emerges for non-phantom accretion to these two objects. Accretion to massless EBWH (i.e., to nonzero Wheelerian mass) shares the same patterns as those of the massive EBWH; hence there is no way to distinguish massive and massless cases by means of accretion flow. The contrasting mass variations due to phantom accretion could be a reflection of the distinct topology of the central objects.

Black holes and large N complex saddles in 3D-3D correspondence

We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions for the two Euclidean supergravity solutions, Bolt± with p = 0, which are Wick rotation of magnetically charged AdS4 black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the F ∧ F-term in the supergravity and the coefficient is proportional to the Chern-Simons invariant of 3-manifold. Combining the holographic computation with 3D-3D relation for twisted indices, we propose a non-trivial mathematical conjecture regarding the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifold.

Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories

This hypothesis is the result of my conviction that science will oneday prove everything in space and time is part of a unification. In "A Brief History of Time", Stephen Hawking wrote, "If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution (of the universe's puzzles) by investigating parts of the problem (such as general relativity and quantum mechanics) in isolation." The goal: to establish a “proof of concept” to which equations can be added. It’s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-8 Klein bottles and Wick rotation works better. The failed cosmologies have impressive points leading to the idea that they’re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but its supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter, dark energy, and electromagnetic-gravitational union. Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.

Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories

This hypothesis is the result of my conviction that science will oneday prove everything in space and time is part of a unification. In "A Brief History of Time", Stephen Hawking wrote, "If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution (of the universe's puzzles) by investigating parts of the problem (such as general relativity and quantum mechanics) in isolation." The goal: to establish a &ldquo;proof of concept&rdquo; to which equations can be added. It&rsquo;s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-8 Klein bottles and Wick rotation works better. The failed cosmologies have impressive points leading to the idea that they&rsquo;re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but its supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter, dark energy, and electromagnetic-gravitational union. Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.

Cosmological solutions, a new wick-rotation, and the first law of thermodynamics

We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a “triple Wick-rotation” by analytically continuing all spacelike directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of $$ \mathcal{N} $$ N = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations.