diff --git a/CHANGES b/CHANGES
index db7d1cf56..495d47199 100644
--- a/CHANGES
+++ b/CHANGES
@@ -18,6 +18,8 @@ Deprecated
 * ``sphinx.builders.gettext.POHEADER``
 * ``sphinx.io.SphinxStandaloneReader.app``
 * ``sphinx.io.SphinxStandaloneReader.env``
+* ``sphinx.util.texescape.tex_escape_map``
+* ``sphinx.util.texescape.tex_hl_escape_map_new``
 
 Features added
 --------------
diff --git a/doc/extdev/deprecated.rst b/doc/extdev/deprecated.rst
index 8c201b525..958f4ee4d 100644
--- a/doc/extdev/deprecated.rst
+++ b/doc/extdev/deprecated.rst
@@ -41,6 +41,16 @@ The following is a list of deprecated interfaces.
      - 4.0
      - ``sphinx.io.SphinxStandaloneReader.setup()``
 
+   * - ``sphinx.util.texescape.tex_escape_map``
+     - 2.3
+     - 4.0
+     - ``sphinx.util.texescape.escape()``
+
+   * - ``sphinx.util.texescape.tex_hl_escape_map_new``
+     - 2.3
+     - 4.0
+     - ``sphinx.util.texescape.hlescape()``
+
    * - ``sphinx.domains.math.MathDomain.add_equation()``
      - 2.2
      - 4.0
diff --git a/sphinx/builders/latex/__init__.py b/sphinx/builders/latex/__init__.py
index 9c34b5568..02f147e40 100644
--- a/sphinx/builders/latex/__init__.py
+++ b/sphinx/builders/latex/__init__.py
@@ -440,10 +440,12 @@ def default_latex_use_xindy(config: Config) -> bool:
 
 def default_latex_documents(config: Config) -> List[Tuple[str, str, str, str, str]]:
     """ Better default latex_documents settings. """
+    project = texescape.escape(config.project, config.latex_engine)
+    author = texescape.escape(config.author, config.latex_engine)
     return [(config.master_doc,
              make_filename_from_project(config.project) + '.tex',
-             texescape.escape_abbr(texescape.escape(config.project)),
-             texescape.escape_abbr(texescape.escape(config.author)),
+             texescape.escape_abbr(project),
+             texescape.escape_abbr(author),
              'manual')]
 
 
diff --git a/sphinx/ext/todo.py b/sphinx/ext/todo.py
index d2a8a666d..99dc02d3d 100644
--- a/sphinx/ext/todo.py
+++ b/sphinx/ext/todo.py
@@ -27,10 +27,9 @@ from sphinx.domains import Domain
 from sphinx.environment import BuildEnvironment
 from sphinx.errors import NoUri
 from sphinx.locale import _, __
-from sphinx.util import logging
+from sphinx.util import logging, texescape
 from sphinx.util.docutils import SphinxDirective
 from sphinx.util.nodes import make_refnode
-from sphinx.util.texescape import get_escape_func
 from sphinx.writers.html import HTMLTranslator
 from sphinx.writers.latex import LaTeXTranslator
 
@@ -299,11 +298,12 @@ def depart_todo_node(self: HTMLTranslator, node: todo_node) -> None:
 
 def latex_visit_todo_node(self: LaTeXTranslator, node: todo_node) -> None:
     if self.config.todo_include_todos:
-        escape = get_escape_func(self.config.latex_engine)
         self.body.append('\n\\begin{sphinxadmonition}{note}{')
         self.body.append(self.hypertarget_to(node))
+
         title_node = cast(nodes.title, node[0])
-        self.body.append('%s:}' % escape(title_node.astext()))
+        title = texescape.escape(title_node.astext(), self.config.latex_engine)
+        self.body.append('%s:}' % title)
         node.pop(0)
     else:
         raise nodes.SkipNode
diff --git a/sphinx/highlighting.py b/sphinx/highlighting.py
index 0a6cf8d6e..6804b9de0 100644
--- a/sphinx/highlighting.py
+++ b/sphinx/highlighting.py
@@ -27,8 +27,7 @@ from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.ext import doctest
 from sphinx.locale import __
 from sphinx.pygments_styles import SphinxStyle, NoneStyle
-from sphinx.util import logging
-from sphinx.util.texescape import get_hlescape_func, tex_hl_escape_map_new
+from sphinx.util import logging, texescape
 
 if False:
     # For type annotation
@@ -114,7 +113,7 @@ class PygmentsBridge:
             # first, escape highlighting characters like Pygments does
             source = source.translate(escape_hl_chars)
             # then, escape all characters nonrepresentable in LaTeX
-            source = source.translate(tex_hl_escape_map_new)
+            source = texescape.escape(source, self.latex_engine)
             return '\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n' + \
                    source + '\\end{Verbatim}\n'
 
@@ -194,8 +193,7 @@ class PygmentsBridge:
         if self.dest == 'html':
             return hlsource
         else:
-            escape = get_hlescape_func(self.latex_engine)
-            return escape(hlsource)
+            return texescape.hlescape(hlsource, self.latex_engine)
 
     def get_stylesheet(self):
         # type: () -> str
diff --git a/sphinx/util/template.py b/sphinx/util/template.py
index 3a43db9a5..e6e72d079 100644
--- a/sphinx/util/template.py
+++ b/sphinx/util/template.py
@@ -9,6 +9,7 @@
 """
 
 import os
+from functools import partial
 from typing import Dict, List, Union
 
 from jinja2.loaders import BaseLoader
@@ -69,8 +70,9 @@ class LaTeXRenderer(SphinxRenderer):
         super().__init__(template_path)
 
         # use texescape as escape filter
-        self.env.filters['e'] = texescape.get_escape_func(latex_engine)
-        self.env.filters['escape'] = texescape.get_escape_func(latex_engine)
+        escape = partial(texescape.escape, latex_engine=latex_engine)
+        self.env.filters['e'] = escape
+        self.env.filters['escape'] = escape
         self.env.filters['eabbr'] = texescape.escape_abbr
 
         # use JSP/eRuby like tagging instead because curly bracket; the default
diff --git a/sphinx/util/texescape.py b/sphinx/util/texescape.py
index e3c45adb4..f490c25c1 100644
--- a/sphinx/util/texescape.py
+++ b/sphinx/util/texescape.py
@@ -9,7 +9,10 @@
 """
 
 import re
-from typing import Callable, Dict
+from typing import Dict
+
+from sphinx.deprecation import RemovedInSphinx40Warning, deprecated_alias
+
 
 tex_replacements = [
     # map TeX special chars
@@ -84,47 +87,38 @@ unicode_tex_replacements = [
     ('₉', r'\(\sb{\text{9}}\)'),
 ]
 
-tex_escape_map = {}  # type: Dict[int, str]
-tex_escape_map_without_unicode = {}  # type: Dict[int, str]
-tex_replace_map = {}
-tex_hl_escape_map_new = {}  # type: Dict[int, str]
-tex_hl_escape_map_new_without_unicode = {}  # type: Dict[int, str]
+tex_replace_map = {}  # type: Dict[int, str]
+
+_tex_escape_map = {}  # type: Dict[int, str]
+_tex_escape_map_without_unicode = {}  # type: Dict[int, str]
+_tex_hlescape_map = {}  # type: Dict[int, str]
+_tex_hlescape_map_without_unicode = {}  # type: Dict[int, str]
 
 
-def get_escape_func(latex_engine: str) -> Callable[[str], str]:
-    """Get escape() function for given latex_engine."""
-    if latex_engine in ('lualatex', 'xelatex'):
-        return escape_for_unicode_latex_engine
-    else:
-        return escape
+deprecated_alias('sphinx.util.texescape',
+                 {
+                     'tex_escape_map': _tex_escape_map,
+                     'tex_hl_escape_map_new': _tex_hlescape_map,
+                 },
+                 RemovedInSphinx40Warning)
 
 
-def escape(s: str) -> str:
+def escape(s: str, latex_engine: str = None) -> str:
     """Escape text for LaTeX output."""
-    return s.translate(tex_escape_map)
-
-
-def escape_for_unicode_latex_engine(s: str) -> str:
-    """Escape text for unicode supporting LaTeX engine."""
-    return s.translate(tex_escape_map_without_unicode)
-
-
-def get_hlescape_func(latex_engine: str) -> Callable[[str], str]:
-    """Get hlescape() function for given latex_engine."""
     if latex_engine in ('lualatex', 'xelatex'):
-        return hlescape_for_unicode_latex_engine
+        # unicode based LaTeX engine
+        return s.translate(_tex_escape_map_without_unicode)
     else:
-        return hlescape
+        return s.translate(_tex_escape_map)
 
 
-def hlescape(s: str) -> str:
+def hlescape(s: str, latex_engine: str = None) -> str:
     """Escape text for LaTeX highlighter."""
-    return s.translate(tex_hl_escape_map_new)
-
-
-def hlescape_for_unicode_latex_engine(s: str) -> str:
-    """Escape text for unicode supporting LaTeX engine."""
-    return s.translate(tex_hl_escape_map_new_without_unicode)
+    if latex_engine in ('lualatex', 'xelatex'):
+        # unicode based LaTeX engine
+        return s.translate(_tex_hlescape_map_without_unicode)
+    else:
+        return s.translate(_tex_hlescape_map)
 
 
 def escape_abbr(text: str) -> str:
@@ -134,19 +128,19 @@ def escape_abbr(text: str) -> str:
 
 def init() -> None:
     for a, b in tex_replacements:
-        tex_escape_map[ord(a)] = b
-        tex_escape_map_without_unicode[ord(a)] = b
+        _tex_escape_map[ord(a)] = b
+        _tex_escape_map_without_unicode[ord(a)] = b
         tex_replace_map[ord(a)] = '_'
 
     for a, b in unicode_tex_replacements:
-        tex_escape_map[ord(a)] = b
+        _tex_escape_map[ord(a)] = b
         tex_replace_map[ord(a)] = '_'
 
     for a, b in tex_replacements:
         if a in '[]{}\\':
             continue
-        tex_hl_escape_map_new[ord(a)] = b
-        tex_hl_escape_map_new_without_unicode[ord(a)] = b
+        _tex_hlescape_map[ord(a)] = b
+        _tex_hlescape_map_without_unicode[ord(a)] = b
 
     for a, b in unicode_tex_replacements:
-        tex_hl_escape_map_new[ord(a)] = b
+        _tex_hlescape_map[ord(a)] = b
diff --git a/sphinx/writers/latex.py b/sphinx/writers/latex.py
index 5facdc40c..5641c08f8 100644
--- a/sphinx/writers/latex.py
+++ b/sphinx/writers/latex.py
@@ -28,11 +28,11 @@ from sphinx.deprecation import (
 from sphinx.domains.std import StandardDomain
 from sphinx.errors import SphinxError
 from sphinx.locale import admonitionlabels, _, __
-from sphinx.util import split_into, logging
+from sphinx.util import split_into, logging, texescape
 from sphinx.util.docutils import SphinxTranslator
 from sphinx.util.nodes import clean_astext, get_prev_node
 from sphinx.util.template import LaTeXRenderer
-from sphinx.util.texescape import get_escape_func, tex_replace_map
+from sphinx.util.texescape import tex_replace_map
 
 try:
     from docutils.utils.roman import toRoman
@@ -500,9 +500,6 @@ class LaTeXTranslator(SphinxTranslator):
         self.compact_list = 0
         self.first_param = 0
 
-        # escape helper
-        self.escape = get_escape_func(self.config.latex_engine)
-
         # sort out some elements
         self.elements = self.builder.context.copy()
 
@@ -736,6 +733,9 @@ class LaTeXTranslator(SphinxTranslator):
         # type: (str) -> str
         return '\\autopageref*{%s}' % self.idescape(id)
 
+    def escape(self, s: str) -> str:
+        return texescape.escape(s, self.config.latex_engine)
+
     def idescape(self, id):
         # type: (str) -> str
         return '\\detokenize{%s}' % str(id).translate(tex_replace_map).\
diff --git a/tests/test_build_latex.py b/tests/test_build_latex.py
index 0ebcd0b62..38e99f48a 100644
--- a/tests/test_build_latex.py
+++ b/tests/test_build_latex.py
@@ -1414,6 +1414,7 @@ def test_default_latex_documents():
                      'project': 'STASI™ Documentation',
                      'author': "Wolfgang Schäuble & G'Beckstein."})
     config.init_values()
+    config.add('latex_engine', None, True, None)
     expected = [('index', 'stasi.tex', 'STASI™ Documentation',
                  r"Wolfgang Schäuble \& G'Beckstein.\@{}", 'manual')]
     assert default_latex_documents(config) == expected