Session J02: Gravitation

Bootstrap bounds on hyperbolic manifolds

The conformal bootstrap is a method for finding bounds on the scaling dimensions of operators in conformal field theories by using general consistency conditions and convex optimization. In this talk, I will discuss a version of the conformal bootstrap that can be used to obtain bounds on the eigenvalues of the Laplacian operator on hyperbolic manifolds. In two dimensions, some of these bounds are almost saturated by particular Riemann surfaces.   

Action for Causal Set Theory

Causal Set Theory(CST) is one of many approaches to quantum gravity that assumes that continuous spacetime is an emergent phenomenon rather than fundamental. In CST, Spacetime is defined through the set of collections of discrete spacetime points which are related only by causality (also known as causal sets). These sets are the fundamental structure of spacetime. These sets must, however, provide us with continuum spacetime under continuum approximation. The kinematics of this theory has been worked out. One of many ways to build the dynamics for CST is by searching for a causal set analog of scalar curvature action.

This presentation aims to compare two ways of calculating these causal set versions of Scalar Curvature Action. One method is given by Bennincasa-Dowker action which introduces a nonlocal retarted linear operator on a scalar field of a causal set. This operator under local approximation can provide us with scalar curvature which in turn can be used to find the action. The other method is given by Dr. Luca Bombelli and Dr. Benjamin Pilgrim in the paper" A Tale of two Action". Using the expectation value of the 3-length chain, one can find its relationship with scalar curvature in curved spacetime. This can be used to define Chain Action. I will discuss all the pros and cons of these two methods in the presentation.   

Curved spacetime in the causal set approach to quantum gravity.

Causal Set theory is an approach to quantum gravity. In the viewpoint of causal set theory, the spacetime continuum is discrete rather than continuous at the most fundamental level. The discrete points in a causal set can approximate a spacetime continuum if they can be embedded in a manifold such that the causal structure between every pair of points is preserved. We sprinkled points inside a causal diamond uniformly with the use of a computer-generated random number r ∈ [0 1]. These sprinklings were done for the number of points ranging from 100 to 1000 at an interval of 100 points. The sprinkling of points randomly and uniformly inside the causal diamond, which was dictated by the spacetime metric, was used to obtain the relations matrix R. Finally, with the use of this relations matrix R, chain-length distributions were obtained. Chains of length greater than two were used to acquire information about the dimension and curvature of the manifold the causal set was embedded into. The dimension was estimated with the aid of chains of length three for two and higher-dimensional flat spacetime manifold. Similarly, the scalar curvature of several spacetime manifolds (Minkowski, de Sitter, and Anti-de Sitter) was approximated using chains of length three. These results averaged over fifty causal sets with the number of points ranging from 100 to 1000 with 100-point increments, demonstrated excellent accuracy with minimal fluctuations from the continuum limit even for a 100-point causal set.   

Short-Range Forces Due to Lorentz-Symmetry Violation: Going Beyond The Standard Yukawa Parametrization

Short-range modifications to Newtonian gravity arising from spacetime-symmetry breaking are studied in this work. The first non-perturbative, i.e., to all orders in coefficients for Lorentz-symmetry breaking, are constructed in the Newtonian limit. We make use of the generic symmetry-breaking terms modifying the gravity sector and examine the isotropic coefficient limit. In which we derive the coefficients in the weak gravity limit using Green function methods. The results show new kinds of force law corrections, going beyond the standard Yukawa parameterization. Further, there are ranges of the values of the coefficients that could make the resulting forces large compared to the Newtonian prediction at short distances. Experimental signals are discussed for typical test mass arrangements.   

Capillary Action as a model for Filaments in Space

Einstein's first writing was about capillary action, as there was no work done to make water rise in trees. Work was the cornerstone of Physics in those years, and was the crux of Geometrical Physics, as pointed out by Robert Millikan, who was most famous for his oil drop experiment. The balancing of forces showed up in capillary action, but not as Einstein envisioned it. Einstein thought that a gas flowed in the capillaries, along with water. Later in "The Photoelectric Effect", the gas was replaced by "holes." The importance of "holes" was firmly established by Dirac. In Outer Space there is once again a balance of "Holes" and "Matter." There are many types of holes, those that come from pair production, show up initially as positrons, which is antimatter. This author proposed that the antimatter, evaporates into holes as time passes, since Feynman noted that antimatter could be viewed as matter traveling backwards in time. An interesting phenomenon was proposed by Hawking, where Matter fell into a Black Hole (another type of hole) and antimatter was created outside the horizon, and escaped the pull of the Black Hole. There was a time that antimatter was thought to travel away from gravity, but that has largely been dismissed. Antimatter may travel out of black holes in the form of "Holes." One of the interesting places that one sees the traveling of holes is in capillary action in trees. The water molecule evaporates from the leave (it can evaporate from a cut stump as well, it is a very interesting thing to observe, as the action is so strong, that the water puddles on top of the stump). When the water evaporates from the tree, one can surmise that a "Hole" is formed which travels down the capillary and into the soil, which then attracts other molecules of water, and perhaps nutrients and gases, via the Photoelectric Effect. This "negative energy field", is nearly impossible to detect, but leaves evidence in the soil. "Electron holes" capillate out of Black Holes in a similar method. There is an interesting effect that can be surmised, and that is with "White Holes." In "White Holes", "electron holes" capillate into the hole and matter flows outward from it. "Holes", can be viewed as the fabric of SpaceTime, "Black Holes" creating SpaceTime by capillating "electron hole" outward, eating matter, and "White Holes" eat SpaceTime and produce matter.   

Spacetime as a evolving causal set

Causal set theory is a discrete approach to quantum gravity. Spacetime continuum is replaced by discrete and locally finite posets, causal sets. The classical sequential growth (CSG) dynamics by Rideout and Sorkin is a framework for growing a causal set based upon physical conditions. In the growth process, elements are added one at a time, and the new element's past structure is determined by a sequence of parameters. We explore whether or not causal sets generated in such a fashion are manifoldlike (representing physical spacetimes) using chain distributions. We will show the results of causal sets generated by several subfamilies of the dynamics. Our simulations support the conjecture that the universe go through an initial stage of being a random tree-like structure. We also try to find a connection between CSG dynamics and actions. We will present a scheme to explore how the birth of an new element alters the action of an manifoldlike causal set and some preliminary results.