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Weicheng Zhao

Publications and source records attributed to Weicheng Zhao.

11 recordsLinked to original sources

Exact Toda Black Holes of Rank-2 Lie Groups

We consider Einstein gravity coupled to two Maxwell fields and one dilatonic scalar, and construct spherically-symmetric and static black holes that are charged under both Maxwell fields in general $D$ dimensions. We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. We devise a brute-force approach to obtain the most general but remarkably elegant solutions to the Toda equations. This allows us to construct exact black holes associated with all the rank-2 Lie groups. We study their thermodynamics and verify explicitly an earlier claim in the literature that all these thermodynamic quantities can be derived without having to solve for these black hole solutions.

hep-th

Cortex AISQL: A Production SQL Engine for Unstructured Data

Snowflake's Cortex AISQL is a production SQL engine that integrates native semantic operations directly into SQL. This integration allows users to write declarative queries that combine relational operations with semantic reasoning, enabling them to query both structured and unstructured data effortlessly. However, making semantic operations efficient at production scale poses fundamental challenges. Semantic operations are more expensive than traditional SQL operations, possess distinct latency and throughput characteristics, and their cost and selectivity are unknown during query compilation. Furthermore, existing query engines are not designed to optimize semantic operations. The AISQL query execution engine addresses these challenges through three novel techniques informed by production deployment data from Snowflake customers. First, AI-aware query optimization treats AI inference cost as a first-class optimization objective, reasoning about large language model (LLM) cost directly during query planning to achieve 2-8$\times$ speedups. Second, adaptive model cascades reduce inference costs by routing most rows through a fast proxy model while escalating uncertain cases to a powerful oracle model, achieving 2-6$\times$ speedups while maintaining 90-95% of oracle model quality. Third, semantic join query rewriting lowers the quadratic time complexity of join operations to linear through reformulation as multi-label classification tasks, achieving 15-70$\times$ speedups with often improved prediction quality. AISQL is deployed in production at Snowflake, where it powers diverse customer workloads across analytics, search, and content understanding.

cs.DB

Non-Asymptotic Performance Analysis of DOA Estimation Based on Real-Valued Root-MUSIC

This paper presents a systematic theoretical performance analysis of the Real-Valued root-MUSIC (RV-root-MUSIC) algorithm under non-asymptotic conditions. A well-known limitation of RV-root-MUSIC is the estimation ambiguity caused by mirror roots, which are typically suppressed using conventional beamforming (CBF). By leveraging the equivalent subspace constructed through the conjugate extension method and exploiting the equivalence of perturbations for true and mirror roots, this work provides a comprehensive study of three key aspects: noise subspace perturbation, true-root perturbation, and mirror-root perturbation. A statistical model is established, and generalized perturbation expressions are derived. Monte Carlo simulations confirm the correctness and effectiveness of the theoretical results. The analysis provides a rigorous foundation for parameter optimization in Direction-of-Arrival (DOA) estimation, with applications in radar, wireless communications, and intelligent sensing.

cs.PF

Five dimensional Weyl double copy

The Weyl double copy (WDC) relation connects the Weyl tensor of the gravity theory and the field strength tensor of the Maxwell theory, which provides a concrete realization of the classical double copy. Although intensively investigated, the WDC is only limited in four-dimensional spacetime. In this Letter, we generalize the WDC relation to five-dimensional spacetime, which offers the first example of the WDC in higher dimensions. We show that a special class of five-dimensional type N vacuum solutions admits a special class of degenerate Maxwell field that squares to give the Weyl tensor. The five-dimensional WDC relation defines a scalar field that satisfies the source-free Klein-Gordon equation on the curved background. We further verify that for five-dimensional pp-wave solution and Kundt solutions, the Maxwell fields and the scalar fields also satisfy the Maxwell's equations and the wave equation on five-dimensional Minkowski spacetime.

hep-th

Twisting asymptotic symmetries and algebraically special vacuum solutions

In this paper, we study asymptotic symmetries and algebraically special exact solutions in the Newman-Penrose formalism. Removing the hypersurface orthogonal condition in the well studied Newman-Unti gauge, we obtain a generic asymptotic solution space which includes all possible origins of propagating degree of freedom. The asymptotic symmetry of the generalized system extends the Weyl-BMS symmetry by two independent local Lorentz transformations with non-trivial boundary charges, which reveals new boundary degrees of freedom. The generalized Newman-Unti gauge includes algebraically special condition in its most convenient form. Remarkably, the generic solutions satisfying the algebraically special condition truncate in the inverse power of radial expansions and the non-radial Newman-Penrose equations are explicitly solved at any order. Hence, we provide the most general algebraically special solution space and the derivation is self-contained in the Newman-Penrose formalism. The asymptotic symmetry with respect to the algebraically special condition is the standard Weyl-BMS symmetry and the symmetry parameters consist only the integration constant order. We present the Kerr solution and Taub-NUT solution in the generalized Newman-Unti gauge in a simple form.

gr-qc

Weyl double copy in type D spacetime in four and five dimensions

In this paper, we present a second realization of the Weyl double copy (WDC) in four-dimensional algebraic type D spacetime. We show that any type D vacuum solution admits an algebraically general Maxwell scalar on the curved background that squares to give the Weyl scalar. The WDC relation defines a scalar field that satisfies the Klein-Gordon equation sourced by the Weyl scalar on the curved background. We then extend the type D WDC to five dimensions.

hep-th

Notes on no black hole theorem in three dimensional gravity

In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates system to 3D gravity, we show that the no black hole theorem is manifest in the NP equations. We further study in detail the horizon properties of the 3D charged rotating solutions and confirm that a black hole solution requires a negative cosmological constant.

gr-qc

Asymptotic Weyl double copy in Newman-Penrose formalism

In this paper, we provide a self-contained investigation of the Weyl double copy in the Newman-Penrose formalism. We examine the Weyl double copy constraints for the general asymptotically flat solution in the Newman-Unti gauge. We find that two transparent solutions of the asymptotic Weyl double copy constraints lead to truncated solutions for both linearized and Einstein gravity theory where the solutions are in the manifest form of Petrov type N or type D in the Newman-Unti gauge.

hep-th

Null boundary gravitational charges from local Lorentz symmetries

In this paper, we revisit the null boundary gravitational charge in the Newman-Penrose formalism with special emphasis on the charges from local Lorentz transformations. We find that there is one more charge derived from the local Lorentz transformation and the new charge is purely from the Holst term. This reveals a remarkable fact that trivial terms which do not change classical equations of motion can not only affect the boundary degrees of freedom through their contributions to the boundary charges but also have their own rights to create new boundary degrees of freedom.

hep-th

Notes on self-dual gravity

In this paper, we study self-dual gravity in the Newman-Penrose formalism. We specify the self-dual solution space from the Newman-Unti solutions. We show that the asymptotic symmetries of the self-dual gravity are still the (extended) BMS symmetries. We transform the self-dual Taub-NUT solution into the Newman-Unti gauge in analytical form.

gr-qc

Note on the asymptotic structure of Kerr-Schild form

The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild form. In Newman-Unti gauge, we find a generic solution space satisfying the Kerr-Schild form in series expansion around null infinity. The news function in the solution space is chiral and can not lead to a mass loss formula. A class of asymptotically flat complex pp-wave solutions in closed form is obtained from the solution space.

gr-qc